The lower halogens tend to stop the body from reacting to very early cancer cells and removing this blockage can all over sudden hit you with a toxic hammer.
Of course if the thyroid itself has cancer issues this could show as hypo-thyroid[ism]...
Difficult call, personally I would first attempt some detox like coffee enema, ozone, Beck’s and add MSM/Glucosamine to help the liver. But if this doesn’t give you immediate results (even temporary) then maybe think about taking those drugs while continuing with Lugol’s.